Differentiating:
-2cos(x)sin(x)-2cos(y)sin(y)y¹=-sin(2x+2y)(2+2y¹)=-2sin(2x+2y)-2y¹sin(2x+2y).
Divide through by -2:
cos(x)sin(x)+cos(y)sin(y)y¹=sin(2x+2y)+y¹sin(2x+2y).
Now collect the y¹ terms together:
y¹(cos(y)sin(y)-sin(2x+2y))=sin(2x+2y)-cos(x)sin(x).
y¹=(sin(2x+2y)-cos(x)sin(x))/(cos(y)sin(y)-sin(2x+2y)) or (sin(x)cos(x)-sin(2x+2y))/(sin(2x+2y)-sin(y)cos(y)), answer c.